Mauricio Pochettino's men were far from their best, but they did just enough as Eriksen netted a brace to move Spurs level on to 67 points with third-placed Liverpool, who were held by Everton earlier in the day.
Aside from an early Stoke chance, Spurs were on top for most of the first period, though clear-cut opportunities were by no means a regular occurrence.
Son Heung-min wasted their most presentable first-half chance when through on goal – otherwise Stoke's compact defence limited their openings.
Spurs' persistence eventually paid off just after the interval, as they sliced through Stoke and Eriksen got the goal, but their lead lasted just five minutes – Mame Biram Diouf punishing a Hugo Lloris error.
The away side ultimately took all three points, however, with a 63rd-minute Eriksen free-kick going all the way in despite Kane – back in the starting XI for the first time since March 11 due to an ankle injury – trying to claim the goal, and Spurs held firm in the face of Stoke's late onslaught.
Despite Kane's return to the starting XI, Spurs were guilty of making a laboured start and they were nearly punished in the 12th minute, when Erik Pieters found Diouf with a low cross, only for the Senegalese forward to guide his effort over while stretching.